Harris County Republicans concerned about Trump's impact at the top of the ticket

Of those interviewed, 41 percent said they supported Trump, while 38 percent would prefer Clinton.

Libertarian candidate Gary Johnson took four percent in the poll, while Jill Stein, the Green Party candidate, took a single percentage point. Eleven percent were still undecided, with three percent said they wouldn't vote for any of them.

Trump's lead of three percent is statistically significant, according to UH pollsters, because no Republican presidential candidate since 2000 has failed to carry Texas by less than 11 percentage points.

Those polled reflected the state's racial and ethnic composition based on the 2008 and 2012 presidential elections.